相关论文: Examples of infinitesimal non-trivial accumulation…

We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on $T^2\times S^3$ and certain related manifolds. These structures occur in bouquets and exhaust the Sasaki cones…

Given a volume preserving dynamical system with non-compact phase space, one is sometimes interested in special subsets of its wandering set. One example from celestial mechanics is the set of initial values leading to collision. Another…

Let $k$ be an algebraically closed field and $Q$ be an acyclic quiver with $n$ vertices. Consider the category ${\rm rep}(Q)$ of finite dimensional representations of $Q$ over $k$. The exceptional representations of $Q$, that is, the…

We generalise surface cluster algebras to the case of infinite surfaces where the surface contains finitely many accumulation points of boundary marked points. To connect different triangulations of an infinite surface, we consider infinite…

We characterize a $k$-th accumulation point of pseudo-effective thresholds of $n$-dimensional varieties as certain invariant associates to a numerically trivial pair of an $(n-k)$-dimensional variety. This characterization is applied…

Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…

In their papers, Leonetti, Russo, Somaglia, Menet and Papathanasiou posed the question of whether there exists an infinite dimensional vector space of sequences in $\ell_\infty$ having (except for the zero sequence) an even amount of…

An extremal $k$-packing is a collection of $k$ mutually disjoint metric discs, embedded in a surface, whose radius is maximal for the given topology. We study compact non-orientable surfaces of genus $g\ge 3$ containing extremal…

For any dimension $d\geq 3$ we construct $C^{1}$-open subsets of the space of $C^{3}$ vector fields such that the flow associated to each vector field is Axiom A and exhibits a non-trivial attractor which mixes exponentially with respect to…

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

We obtain that the nonzero accumulation points of the set of 3-fold canonical thresholds $\ct(X,S)$ are precisely $1/k$ where $k\ge 2$ is an integer and $S$ is an effective integral divisor of a projective 3-fold $X$ with only terminal…

We prove that for every three-dimensional vector field, either it can be accumulated by Morse-Smale ones, or it can be accumulated by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit in the $C^1$ topology.

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit…

Over an arbitrary field of characteristic different from $2$ admitting an anisotropic torsion $3$-fold Pfister form, we apply a construction due to Merkurjev to produce an algebra with orthogonal involution of degree $6$ which admits proper…

We give a number of examples of pairs of non-compact surfaces which are isoscattering, and which are exceptionally simple in one or more senses. We give examples which are of small genus with a small number of ends, and also examles which…

We prove that, for $q$ odd, a set of $q+2$ points in the projective plane over the field with $q$ elements has at least $2q-c$ odd secants, where $c$ is a constant and an odd secant is a line incident with an odd number of points of the…

An explanation is given for the initially surprising ubiquity of separating sets in normal complex surface germs. It is shown that they are quite common in higher dimensions too. The relationship between separating sets and the geometry of…

Percolation on a one-dimensional lattice and fractals such as the Sierpinski gasket is typically considered to be trivial because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel…

We study sets of nontypical points under the map $f_\beta \mapsto \beta x $ mod 1, for non-integer $\beta$ and extend our results from [F\"arm, Persson, Schmeling, 2010] in several directions. In particular we prove that sets of points…

For each vector $x\in \ell^{\infty}$, we can define the non-empty compact set $L_x$ of accumulation points of $x$. Given an infinite subset $A$ of $\mathbb{N}\backslash\{1\}$, we can therefore investigate under which conditions on $A$, the…